As the title says, what happens if I develop a color film exactly as I would do with a black and white film?
You can develop E6 and C41 slide or negative film with B&W developers and get monochromatic results. With Kodak film you'll have the orange cast, but you can still scan or print from the negative.
I've seen mention of people using Acufine/Diafine and Rodinal, but never tried it myself. Good examples here: Cross-processing colour film in b&w chemicals
You can also use C41 processing on B&W film if you skip the bleach step, which would wipe out anything on the negative.